Fourier Basis Mapping: A Time-Frequency Learning Framework for Time Series Forecasting
This work addresses forecasting accuracy issues for practitioners in fields like finance or climate, though it is incremental as it builds on existing Fourier and deep learning methods.
The paper tackles inconsistent frequency interpretation and temporal information loss in Fourier-based time series forecasting by introducing Fourier Basis Mapping (FBM), which integrates time-frequency features and achieves state-of-the-art performance on diverse real-world datasets.
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency components can be regarded as the coefficients of cosine and sine basis functions at tiered frequency levels, respectively. We find that existing Fourier-based methods face inconsistent starting cycles and inconsistent series length issues. They fail to interpret frequency components precisely and overlook temporal information. Accordingly, the novel Fourier Basis Mapping (FBM) method addresses these issues by integrating time-frequency features through Fourier basis expansion and mapping in the time-frequency space. Our approach extracts explicit frequency features while preserving temporal characteristics. FBM supports plug-and-play integration with various types of neural networks by only adjusting the first initial projection layer for better performance. First, we propose FBM-L, FBM-NL, and FBM-NP to enhance linear, MLP-based, and Transformer-based models, respectively, demonstrating the effectiveness of time-frequency features. Next, we propose a synergetic model architecture, termed FBM-S, which decomposes the seasonal, trend, and interaction effects into three separate blocks, each designed to model time-frequency features in a specialized manner. Finally, we introduce several techniques tailored for time-frequency features, including interaction masking, centralization, patching, rolling window projection, and multi-scale down-sampling. The results are validated on diverse real-world datasets for both long-term and short-term forecasting tasks with SOTA performance.